Question

The Sisyphean Company has a bond outstanding with a face value of $1,000 that reaches maturity in 5 years. The bond certificate indicates that the stated coupon rate for this bond is 9.8​% and that the coupon payments are to be made semiannually.Assuming the appropriate YTM on the Sisyphean bond is 7.9​%,then the price that this bond trades for will be closest​ to:

A 1,508

B 1,293

C 862

D 1,077

Answer 1

Answer is $1,077

Face Value = $1,000

Annual Coupon Rate = 9.80%
Semiannual Coupon Rate = 4.90%
Semiannual Coupon = 4.90% * $1,000
Semiannual Coupon = $49

Time to Maturity = 5 years
Semiannual Period = 10

Annual YTM = 7.90%
Semiannual YTM = 3.95%

Price of Bond = $49 * PVIFA(3.95%, 10) + $1,000 * PVIF(3.95%, 10)
Price of Bond = $49 * (1 - (1/1.0395)^10) / 0.0395 + $1,000 * (1/1.0395)^10
Price of Bond = $49 * 8.131122 + $1,000 * 0.678821
Price of Bond = $1,077